On the structure of split involutive Hom-Lie color algebras
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Valiollah Khalili [1]
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[1] Arak University
Arak University
Irán
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- Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 1, 2019, págs. 61-77
- Idioma: inglés
- DOI: 10.33044/revuma.v60n1a05
- Enlaces
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Resumen
In this paper we study the structure of arbitrary split involutive regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split involutive regular Hom-Lie color algebra L is of the form L=U⊕∑[α∈Π/∼I[α], with U a subspace of the involutive abelian subalgebra H and any I[α], a well-described involutive ideal of L, satisfying [I[α], I[β]]=0 if [α]≠[β]. Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its minimal involutive ideals, each one being a simple split involutive regular Hom-Lie color algebra. Finally, an example will be provided to characterise the inner structure of split involutive Hom-Lie color algebras.
